JEE Main · 2025 · 02 Apr 2025 · Shift 2 · Electrostatics

Consider a circular loop that is uniformly charged and has a radius

a 2

. Find the position along the positive z-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy-plane at the origin :

(A) $\frac{a}{2}$
(B) $\frac{a}{2}$
(C)a✓ Correct
(D)0

Answer: (C)

Solution

For a uniformly charged ring of radius R, the electric field along the axis at distance x from the center is:

E = \frac{k Q x}{( x ^{2} + R ^{2} ) ^{3/2}}

To find maximum, differentiate with respect to x and set equal to zero:

\frac{d E}{d x} = 0

This gives:

x = \frac{R}{2}

For the given ring with radius

R = a 2

x = \frac{a 2}{2} = a

Therefore, the electric field is maximum at position x = a along the z-axis.

JEE Main · 2025 · 02 Apr 2025 · Shift 2 · Single correct option

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